The numerical solution of Boundary Value Problems usually requires the use of an adaptive mesh selection strategy. For this reason, when a Linear Multistep Method is considered, a dynamic computation of its coefficients is necessary. This leads to solve linear systems which can be expressed in different forms, depending on the polynomial basis used to impose the order conditions. In this paper, we compare the accuracy of the numerically computed coefficients for three different formulations. For all the considered cases Vandermonde systems on general abscissae are involved and they are always solved by the Bj ̈rk-Pereyra algorithm. An adaptation of the forward error analysis given in [8, 9] is proposed whose significance is confirmed by the numerical results.
Numerical aspects of the coefficient computation for LMMs
ACETO, LIDIA;
2008-01-01
Abstract
The numerical solution of Boundary Value Problems usually requires the use of an adaptive mesh selection strategy. For this reason, when a Linear Multistep Method is considered, a dynamic computation of its coefficients is necessary. This leads to solve linear systems which can be expressed in different forms, depending on the polynomial basis used to impose the order conditions. In this paper, we compare the accuracy of the numerically computed coefficients for three different formulations. For all the considered cases Vandermonde systems on general abscissae are involved and they are always solved by the Bj ̈rk-Pereyra algorithm. An adaptation of the forward error analysis given in [8, 9] is proposed whose significance is confirmed by the numerical results.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
